The rapid adoption of telematic and fare collection systems from bus operators has enhanced monitoring of bus operations and can potentially improve reliability of transit services. For instance, Automated Vehicle Location (AVL) systems have been broadly deployed and used for monitoring the daily operations since the late 1990s. Owing to the adoption of telematics and fare collection systems, public transport authorities can evaluate the performance of bus operators based on concrete metrics such as the excess waiting times (EWTs) of passengers at stops, the punctual adherence to the planned schedules, the total number of vehicle kilometers traveled, and many more. Early assessments can be found in Strathman et al., “Evaluation of Transit Operations: Data Applications of Tri-Met's Automated Bus Dispatching system,” Transportation (2002), where the Tri-Met's automated bus dispatching system was evaluated using AVL and partial Automated Passenger Counting (APC) data.
Recently, public transport authorities have started using information from telematics and fare collection systems for penalizing bad-performing bus operators and rewarding the best-performing ones using direct monetary incentives. As an example, the introduced Bus Service Reliability Framework (BSRF) in Singapore incentivizes the bus operators by providing 2,000 Singaporean dollars per month for every 0.1 minute improvement of the passenger EWTs. This has motivated bus operators to improve their daily operations by analyzing the generated AVL and AFC datasets or new forms of user-generated data such as social media data or cellular data.
Apart from the analysis of data, this pressure has started to affect the strategic planning which determines the design of the network routes and the tactical planning which consists of the (i) frequency setting; (ii) timetable design and (iii) vehicle and crew scheduling. For instance, reliable frequencies for the bus services can be set using insights from operational AVL and AFC data, and data-driven timetables can be developed using smartcard records generated when passengers board and alight at buses. Besides strategic and tactical planning, bus operators are in need of also improving their operational planning. For instance, bus operators occasionally deploy a variety of near 33 real-time control measures, such as stop-skipping, bus holding at stops, and short-turnings for performing corrective actions when actual operations deviate significantly from the planned schedules. Nevertheless, these corrective measures can cause undesirable secondary effects, such as the increase of in-vehicle travel times due to bus holdings at stops, the increase of deadheading times due to short-turnings, and the increase of passenger inconvenience due to stop-skipping. In addition, such control measures can affect crew schedules, vehicle allocation, or result in “schedule sliding.”
The EWT has its roots to the definition of the Actual Waiting Times (AWT) of passengers at stops. The AWT links the waiting time of passengers at stops with the headways of successive bus trips by assuming that the passenger arrivals at stops are random and therefore the AWT is equal to half the average headway at one stop plus the ratio of the headway variance at that stop to twice the average headway. The EWT is equal to the AWT of passengers at each stop minus the Scheduled Waiting Times (SWT) of passengers at those stops and is widely used by several transport authorities for monitoring purposes (such as Transport for London (TfL) and the Land Transport Authority (LTA) in Singapore).
This pressure from the transport authorities has forced bus operators to introduce a variety of control measures such as bus holding at stops, stop-skipping, short-turnings and more. Reflecting to that, extensive research in this field has tried to provide answers to questions such as which control measures are the most effective, how can control measures be automated, how can operational constraints related to labor and fleet size limitations be satisfied, and how can stochastic nature of the bus operations be modelled? Some conventional methods acknowledge that given the stochastic nature of the bus operations, there might be a need for applying corrective measures such as bus holdings, stop-skipping, etc., during the operational phase. Thus, these methods proactively embed slack times in daily trips in order to add flexibility during the operations. Introducing long slack times though requires more buses for maintaining the same service frequency.
Conventional methods relating to timetable optimization strive to ensure that the departure times of trips are evenly spaced. For instance, a desired even load level can be a target for all running buses at the maximum loading point of trips with the determination of dispatching times for bus trips that do not lead to significant deviations from the desired even headways. The desired even headways are inversely proportional to the predefined line frequencies determined during the frequency settings stage. Generating timetables with evenly spaced departure times can be combined with the additional objective of synchronizing passenger transfers.
Timetable optimization can also be performed by categorization into methods using deterministic travel times and dwell times during the optimization process and method using stochastic travel times and dwell times. Stochastic travel times have been considered for operational control for deriving dynamic bus holding strategies in order to improve the adherence of the operations to the planned schedule. An analytic bus holding model that considers the stochastic nature of vehicle running times and passenger boarding and alightings has been developed by Hickman, “An analytic stochastic model for the transit vehicle holding problem,” Transportation Science (2001).
Conventional methods have proposed simultaneous optimization of bus frequencies and timetables. Additionally, trying to simultaneously determine the route network design, the bus frequencies and the timetable assignment by integrating the strategic and tactical planning phases has been proposed. Conventional methods also attempted decoupling frequency settings problem from the timetabling problem to obtain their solution in a sequential order. Timetable synchronization for developing bus timetables that are synchronized with the rail timetables or other bus timetables has also been proposed. Conventional methods have also developed flexible timetables that provide some buffer time at synchronization points (i.e., passenger transfer stops) in case there is a deviation between the actual and the 74 planned arrival time of any of the bus trips at the transfer stop.
Several studies control only the running and ignore the implications of the computed bus holdings to the next trips that will be operated by the same buses. Two of the most common bus holding strategies are: (i) the one-headway-based control where a bus is held at a bus stop (called also control point if bus holding is allowed only at a limited number of stops) if it is too close to its preceding bus for a time period such that its departure time is equal to the departure time of its preceding trip plus the planned headway between them, and (ii) the two-headway-based control where that estimates also the arrival time of the following bus at the same stop and considers the headways between the preceding and the following bus when computing a holding time.
In conventional methods, stochasticity is introduced at the single holding problem by modeling it as a convex quadratic program in a single variable for including stochasticity at the vehicle running times and passenger boarding and alightings. Also in conventional methods, an approach that tries to hold the buses at specific stops in order to normalize the headways instead of satisfying a specific headway target; thus, resulting to smoother holdings in case of severe traffic disruptions. However, these real-time holding strategies are heuristic in nature and cannot guarantee an improvement in the operations. For this reason, such strategies have been extensively validated with simulations that use normal and lognormal distributions for introducing stochasticity to the link travel times and approximate the effect of the signal control and the traffic congestion. Given their drawback on performing optimizations at the local level, they require high slack times at the scheduling phase for reducing the adverse effects of the bus trips delays due to the bus holding to the future trips.
Also in conventional methods, an approach that tries to minimize the amount of slack time in the schedule instead of trying to minimize the passenger waiting times with local-level optimizations is provided. Those works also considered the headway variability during the day and introduced noise at the link travel times with the use of the normal distribution in order to validate the performance of their holding measures in different scenarios.
The bus holding problem can also be viewed as a rolling-horizon optimization problem. For this case, the minimization of passenger waiting times can be modeled as a deterministic quadratic program. In addition, the operational constraints can also be considered in the formulation of the bus holding problem and acknowledging that every holding time strategy can have an adverse effect to resource limitations related to labor and fleet numbers. Rolling horizon optimization approaches are able to eliminate the slack time requirement from the schedules because they can optimize the bus holding times of a set of buses (i.e., from all the daily bus trips of a service) at the same time.